Strategy
Since this is a dice-based game, success does depend significantly on luck. That being said, a good player will consistently beat a poor player, so there is some tactical and strategic opportunity.
Both choices (which markers to advance, and whether to roll again or not) offer difficult decisions. You can focus on the easy-to-roll but tall columns, such as 6, 7 and 8; or you can focus on the short, but difficult-to-roll columns such as 2 and 12. If your markers are in the shorter columns, you should choose to reroll less frequently, since there is much lower chance of matching your chosen numbers. If another player is close to claiming a column, then you should probably push your luck longer, hoping to steal this column away.
There is significant benefit to keeping the neutral markers off the board for as long as possible. There are typically very few rolls that cause your turn to end when you have off-board neutral markers left.
Having markers on 6, 7, and 8 gives the highest chance of making another successful roll, 91.97%, 1192 rolls out of 1296 (64). Some other combinations have surprisingly high hit rates, e.g. 4,6,8 (and so, 6,8,10) match 91.13%. This match rate is higher than, for example, 5,6,8, at 89.51%, or 5,6,7, at 88.66%. This difference occurs because having a marker on 4 catches the cases where three of four dice are 1's or 2's and the fourth die is a 3 (32 rolls out of 1296). The lowest probability of matching on a reroll is for the set 2,3,12 (or 2,11,12), at 43.83%.
The chance of being able to roll again is often balanced by the relatively low progress gains from rolling common numbers. So, although the match rate for 4,6,8 is just slightly lower than for 6,7,8, you need only seven 4's to capture that column, versus thirteen 7's. This makes 4,6,8 superior to 6,7,8 in a benefit/risk analysis. Choosing markers that are not all 8 or below, or all 6 or above, gives more benefit to risk overall. Also, choosing sets of all even numbers and also avoiding sets of all odd numbers is beneficial. In some combinations, a slightly wider distribution is better. For example, if a player already has markers on the 4 and 6 columns, then placing the third marker on the 10 column is better (88% chance of matching) than on the 9 column (86% chance).
One consideration in assessing how many rolls to make in a given turn is the comparison of the expected gain from rolling to the expected loss from wiping out. The "Can't Stop Odds" linked below show the number of rolls to make for a given combination of up to three columns so that on the last roll the expected loss is no greater than the expected gain. This "expected gain" strategy results in wiping out in about 61% percent of turns in which reaching the end of a column is not a factor. In a computer-aided simulation of competing strategies, a superior strategy was to plan a number of rolls that would wipe out no more than 50% of turns (that is, turns in which reaching the end of a column is not a factor). This later strategy prevailed in 55% of games against a simulated player using the "expected gain" strategy. Still, balancing opportunities to prevail with a risky series of rolls against the wisdom of stopping and holding onto your present gains is the essence of Can't Stop. Players can enjoy the drama of this balance without using any simulations at all.
Read more about this topic: Can't Stop (board Game)
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